Ixigo.com shows you the flights and sends you to the airline website to purchase tickets. Kayak also has an Indian site Kayak.co.in.

Among TAs that would sell the ticket (possibly for a fee, though these are sometimes waived) see Expedia.co.in and cleartrip.com.

As for ensuring that you go via Mumbai, nobody is selling you tickets before you click, so look at the route before clicking to buy (you should carefully examine any itinerary before purchase anyway). Else, you can always do multicity search explicitly asking for Delhi-Mumbai and Mumbai-Goa segments.

Good luck.